$($a$)$ When the vibrator is set to a frequency of $158$ Hz $,$ a standing wave with six loops is formed. What must be the linear mass density of the cord? kg$/$m

$($b$)$ How many loops $($if any$)$ will result if $\backslash ($ m $\backslash )$ is changed to $4\mathrm{.}50$ kg $?($Enter $0$ if no loops form.$)$

$($c$)$ How many loops $($if any$)$ will result if $\backslash ($ m $\backslash )$ is changed to $10\mathrm{.}0$ kg $?($Enter $0$ if no loops form.$)$